REVIEW The relationship between limb morphology, kinematics, and

REVIEW

The relationship between limb morphology, kinematics,and force during running: the evolution of locomotordynamics in lizardsbij_1230 634..651

ERIC J. MCELROY1,2* and STEPHEN M. REILLY2

1Department of Biology, College of Charleston, Charleston, SC 29401, USA2Ohio Center for Ecology and Evolutionary Studies and Department of Biological Sciences,Ohio University, Athens, OH 45701, USA

Received 3 October 2008; accepted for publication 9 January 2009

Terrestrial locomotion occurs via the hierarchical links between morphology, kinematics, force, and center-of-massmechanics. In a phylogenetically broad sample of seven lizard species, we show that morphological variation driveskinematic variation, which, in turn, drives force variation. Species with short limbs use a short stride–highfrequency strategy when running at steady-speed and to change speeds. This link between morphology andkinematics results in relatively small vertical forces during the support phase of the stride cycle. Conversely,species with long limbs use a long stride–low frequency strategy, resulting in large vertical forces during thesupport phase. In view of these findings, we suggest that limb length may predict locomotor energetics in lizardsbecause energetics are largely determined by vertical forces and stride frequency. Additionally, we propose anenergetic trade-off with both long- and short-limbed species paying the most energy to move, whereas intermediate-limbed species move using less energy. Finally, when these traits are mapped onto a lizard phylogeny, we show thatlocomotor functional morphology exhibits both deep phylogenetic effects and contemporary patterns of evolutionaryconvergence. Overall, the present study provides a foundation for testing hypotheses regarding the integration andevolution of functional traits in lizards and animals in general. © 2009 The Linnean Society of London, BiologicalJournal of the Linnean Society, 2009, 97, 634–651.

ADDITIONAL KEYWORDS: biomechanics – force – kinematics – lizard – locomotion – morphology – running.

INTRODUCTION

When animals run, their limbs move in rhythmiccycles to propel them through the terrestrial environ-ment. From an organismal perspective, terrestriallocomotion with limbs requires that variation ofmotor pattern and limb morphology will lead to avariation in stride kinematics, which, in turn, willlead to a variation in limb forces, ultimately leadingto differences in center-of-mass dynamics and loco-motor performance (Russell & Bels, 2001; Reilly,McElroy & Biknevicius, 2007). Thus, quantifyingmorphology, kinematics, and forces in an array ofspecies provides a quantitative framework for under-standing how morphology relates to locomotion, how

complex functional systems evolve, and the ecologicalrelevance of morphology (Arnold, 1983; Reilly &Wainwright, 1994). A myriad of studies have exam-ined variation at the level of limb morphology (Alex-ander et al., 1981; Bertram & Biewener, 1990; Miles,1994; Miles, Losos & Irschick, 2007); limb kinematics(Sukhanov, 1968; Heglund & Taylor, 1988; Strang &Steudel, 1990; White & Anderson, 1994; Irschick &Jayne, 1999; Fischer et al., 2002; Vanhooydonck, VanDamme & Aerts, 2002); and force production (Robertset al., 1998). In addition, some studies have estab-lished that morphology is related to stride kinematics(Strang & Steudel, 1990; White & Anderson, 1994;Irschick & Jayne, 1999; Vanhooydonck et al., 2002)and that stride kinematics are related to forces(Heglund et al., 1982; Full, 1989; Farley, Glasheen& McMahon, 1993; Farley & Ko, 1997; Chen et al.,*Corresponding author. E-mail: [email protected]

Biological Journal of the Linnean Society, 2009, 97, 634–651. With 7 figures

© 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 97, 634–651634

mailto:[email protected]

2006; Reilly et al., 2006). However, no study hassimultaneously examined the inter-relationshipsamong these three levels (morphology, kinematics,and force) across a morphologically diverse sample.The present study aimed to explain patterns ofvariation in the hierarchical relationship amongmorphology, kinematics, and force generation in aphylogenetic array of species with differing limb mor-phology. We note that our discussion of forces is reallyabout the limb reaction forces that the organismproduces, which must be equal and opposite to theground reaction forces (i.e. part of the physical envi-ronment). Thus, limb reaction forces can and doevolve in response to the mechanical demands ofsupporting and propelling the body and are modu-lated by limb morphology and limb kinematics.However, to avoid confusion, and in accordance withprevious studies of locomotor mechanics, we presentground reaction forces.

How must force covary with stride kinematicsand limb morphology? It has been established thatanimals with shorter limbs have to step more often(i.e. higher stride frequency) than longer-limbedanimals to attain fast speeds (Vanhooydonck et al.,2002). In addition, ample studies of ground reactionforces show that, during steady speed locomotion, thesum of vertical force (i.e. vertical impulse) over a fullstride divided by stride time must be equal to bodyweight (Biewener, 2003). However, general compari-sons across speeds show that stride length, stridefrequency, and float distance (kinematic speed-effects)directly influence how force is propagated during thesupport phase of the stride cycle (Biewener, 2003).Thus, species with short limbs should move at highstride frequency and, as a result, produce less verticalforce per ground contact because they have moreground contacts (i.e. higher stride frequency) per unittime. Conversely, species with longer limbs will havefewer support phases over a given time (i.e. low stridefrequency), leading to the necessity of more verticalforce per support to effectively support body weight.The above arguments are based on the physical lawsgoverning locomotion; ground reaction forces must bedetermined by an organism’s morphology and kine-matics. In view of these laws, studies of limb morphol-ogy and kinematics have made a variety of predictionsregarding how morphological and kinematic variationshould dictate ground reaction forces. For example, (1)species taking long strides at low frequency shouldgenerate more force than species taking shorterstrides at higher frequency (Van Damme, Aerts &Vanhooydonck, 1998; Irschick & Jayne, 1999; Aertset al., 2000) and (2) the relative magnitudes of verticaland accelerative force should be good predictors of thedistance travelled during the aerial phase (i.e. floatingdistance) of the stride cycle (Irschick & Jayne, 1999).

However, empirical data testing these hypotheses, andthus clearly demonstrating that ground reactionforces are indeed determined by limb morphology andkinematics, remain scarce. In the present study, wefirst quantify the multivariate patterns in limb skel-etal morphology, stride kinematics, and force profilesfor seven species of terrestrial lizards. Forces arequantified as both impulses integrated over supportduration and peak forces. Then, multivariate statisti-cal analyses test for differences within levels andcorrelations among levels to suggest the morphologi-cal basis for kinematics and locomotor forces. Theresults obtained illustrate how the dynamics betweenlimb length, support duration, and float distancelikely influence the forces applied to the groundduring the support phase of steady-state locomotion.

MATERIAL AND METHODSSTUDY SPECIES

Locomotor morphology and function were quantifiedin the following seven species of lizards (Fig. 1):Laudakia stellio Linnaeus (Agamidae), Opluruscuvieri Gray (Iguanidae), Tropidurus torquatusWied-neuwied (Iguanidae), Eulamprus quoyii Quoyand Gaimard (Scincidae), Tracheloptychus petersiPeters (Cordylidae), Acanthodactylus boskianusDaudin (Lacertidae), and Varanus exanthematicusBosc (Varanidae). These species were chosen foranalysis because they were all capable of high-speedrunning but encompassed a range of limb morpholo-gies. All species were obtained from commercialdealers, except Eulamprus quoyii, which was wild

Figure 1. Phylogeny for the lizards in this study sensuTownsend et al. (2004). Branching nodes are labelled A–Efor discussion of phylogenetic patterns of locomotor func-tional evolution.

EVOLUTION OF LOCOMOTOR DYNAMICS IN LIZARDS 635


caught in Brisbane, Australia. All housing and experi-mental procedures were conducted in accordance withapproved animal use protocols.

MORPHOLOGY

To quantify locomotor morphology, we took ventalview radiographs of multiple individuals per species(samples sizes are shown in Table 1) and measuredthe lengths of the several morphological variables tothe nearest 0.01 mm using digital calipers: snout–vent, humerus, ulna, carpal, third metacarpal, thirdfinger, pectoral girdle width, femur, tibia, tarsal,fourth metatarsal, fourth toe, fifth metatarsal, fifthtoe, pelvis length, and pelvis width (Fig. 2). Thesevariables were used because previous studies havefound that they are related to locomotor function andperformance in lizards (Miles, 1994; Irschick & Jayne,1999; Miles et al., 2007). We used dissecting pins topress the lizards limbs as close to the radiographpaper as possible to minimize the effect of parallax.All specimens were obtained via museum loans(catalogue numbers are provided in the Appendix).

LOCOMOTOR FUNCTION

Data collectionStride kinematics and force were studied as lizardssprinted down a racetrack towards a dark hide box.Running was induced by gently pressing on the tail orhindlimb. Running trials were recorded over a rangeof running speeds, including near-maximum sprintspeed for each species (Table 1). All trials consisted oflizards using running (spring-mass) mechanics and adiagonal-couplet gait. To avoid fatigue effects, eachindividual was run down the racetrack up to threetimes and then allowed to rest and recover for 24 hbefore subsequent trials. All species were maintainedat 36–40 °C for the duration of each trial. Tempera-

ture was checked during each trial with an infra-redlaser thermometer aimed along the body axis.

Stride kinematicsLizards were filmed at 120 or 500 Hz (small, fastlizards required higher frame rates) with high-speedvideo cameras (JVC GRL-9800 and NAC HSV-500 C3)mounted 1 m above the surface of the force platform.Mirrors were mounted on angled walls along each

Table 1. Species sample size for morphology (number of individuals) and locomotor function (number of trials)

MorphologyKinematicsand force

Running speed(m s-1)

Dimensionlessspeed

N N Range Range

Acanthodactylus boskianus 30 6 1.88–0.82 2.81–1.23Eulamprus quoyii 29 10 1.92–0.71 2.87–1.06Laudakia stellio 33 13 2.40–0.82 2.77–0.95Oplurus cuvieri 21 17 1.69–0.59 1.80–0.63Tracheloptychus petersi 12 6 1.41–1.01 1.97–1.42Tropidurus torquatus 7 9 2.62–1.37 3.15–1.65Varanus exanthematicus 13 11 2.54–0.76 2.78–0.83

Figure 2. Ventral radiograph of Laudakia stellio summa-rizing the 16 morphological measurements. 1, snout–vent;2, humerus; 3, ulna; 4, carpal; 5, third metacarpal; 6, thirdfinger; 7, pectoral girdle width; 8, femur; 9, tibia; 10,tarsal; 11, fourth metatarsal; 12, fourth toe; 13, fifth meta-tarsal; 14, fifth toe; 15, pelvis length; 16, pelvis width.Note that when toes were bent (measurements 6, 12, and14), we summed the measures of the length of individualphalanges.

636 E. J. MCELROY and S. M. REILLY


side of the force platform to visualize footfalls. Kine-matic analyses were conducted using APAS, version1.0 Ariel Dynamics, INC. Speed during each trial wasquantified by digitizing the tip of the snout as thelizard crossed seven evenly-spaced lines along thesurface of the racetrack and calculating averagespeed across the entire field of view. Only trials with< 20% difference between any interval speed and theaverage speed were used. The timing of touch-downand lift-off for each limb was recorded in these steadyspeed trials. The velocity and the timing of foot touch-down and lift-off were used to calculate the kinematicvariables: (1) stride length, which is the distancetravelled by the center-of-mass during one entirehindlimb cycle, calculated by multiplying velocity bythe amount of time between ipsilateral hindlimbtouchdowns; (2) stride frequency, which compriseshindlimb strides per second, calculated as the inverseof the amount of time between ipsilateral hindlimbtouchdowns (stride duration); (3) step length, which isthe distance travelled by the center-of-mass when ahindlimb-forelimb couplet contacted the ground, cal-culated as velocity multiplied by the amount of timea couplet contacted the ground; and (4) float distance,which is the distance travelled by the center-of-masswhen no limbs contact the ground, calculated asstride length minus two times step length. Supportduration was defined as the time from the touchdownof the first limb of a couplet (fore or hindlimb) untilthe lift-off of the last of that pair of supporting limbs.

Whole body locomotor forcesGround reaction forces were quantified and using acustom-made force platform based on a strain gauge,spring-blade design (Bertram et al., 1997). Vertical(V), fore-aft (FA), and medio-lateral (ML) groundreaction forces were sampled at 500 Hz using Na-tional Instruments data acquisition hardware andLABVIEW custom designed virtual data samplingand quantification instruments. The 0.6 m (length) by0.2 m (width) force platform surface was flush withthe racetrack surface and located 3–3.6 m along its5.2-m length. The entire surface of the racetrack andplatform was covered with fine grit sandpaper toprevent foot slippage.

From the whole body ground reaction forces, wequantified 13 force variables. These variables describethe shapes and amplitudes of force profiles to bequantitatively compared across species in relation tomorphology and gait (Fig. 3). Peak forces were mea-sured as the maximum force in each direction: peakvertical, braking (negative value), accelerative, andlateral forces (absolute value for lateral to account forleft versus right limb pushes). The remaining ninetime-related variables were measured relative to

support duration (i.e. limb morphology and kinemat-ics affect locomotor forces applied to the substrate bythe limbs). Impulses were measured as the areaunder the force curve (i.e. the numerical integrationof the force over limb contact time) for vertical,braking, accelerative, and lateral directions. Time topeak vertical, braking, accelerative, lateral force, andtime of the braking–accelerative transition point(when the fore–aft force profile switched from nega-

Figure 3. Representative whole body ground reactionforce profiles. Impulses are represented by hatched areas;dotted lines correspond to the peak or time of peak force.1, vertical impulse; 2, braking impulse; 3, accelerativeimpulse; 4, lateral impulse; 5, peak vertical force; 6, peakbraking force; 7, peak accelerative force; 8, peak lateralforce; 9, time to peak vertical force; 10, time to peakbraking force; 11, time to peak accelerative force; 12, timeto peak lateral force; 13, time of braking–accelerativetransition, indicated by a star.



tive to positive values) were also measured and scaledto percentage of support duration.

STATISTICAL ANALYSIS

Prior to statistical analysis, some variables weretransformed to approximate a normal distribution. Allmorphological variables float distance, impulses, andpeak forces were log10 transformed. All other variableswere untransformed.

Correcting for size and speedTo examine the relationship between morphology,stride kinematics, and whole body forces acrossspecies, we had to control for differences in both bodysize and running speeds. Morphology, stride kinemat-ics, and forces are known to covary with body size(Mullineaux et al., 2006), and they covaried with sizein the species in the present study (see Supportinginformation, Table S1). To correct for the effect of bodysize, we regressed morphological variables againstsnout–vent length (both length measurements), kine-matics against body mass, and forces against bodyweight (both force measurements) and used theresiduals from these regression for further analysis.Preliminary analyses showed that regressing kine-matics against body mass versus snout–vent lengthhad no qualitative effect on the results.

Kinematics and force are also known to covary withrunning speed (Riggs et al., 1993; McLaughlin et al.,1996). Speed effects were evident in kinematicsand force variables (see Supporting information,Table S1); thus, we corrected for speed by regressingthe size corrected residuals for each variable (fromthe regression of body mass or weight) against speedand used these residuals for further analysis. Thus,morphological variables were corrected for body size,whereas kinematic and force variables were correctedfor both body size and speed.

Finally, many studies attempt to adjust for speedand size differences across species by comparingeffects at dimensionless speed (Farley et al., 1993).We compared the results of using speed correctedkinematic and force variables (as described above)with a parallel analysis using dimensionless speed.Dimensionless speed was defined as v g-1/2 l-1/2 (wherev is speed, g is gravitation acceleration, and l is leglength) for each trial (Farley et al., 1993). Leg lengthas opposed to hip height (Irschick & Jayne, 1999) wasused because did not have detailed lateral videos fromwhich to estimate hip height. Results from analysesbased on raw speed and dimensionless speed pro-duced the same statistical outcomes for the multi-variate analyses relating morphology, kinematics, andforces. Thus, we report the results from analysesbased on raw speed.

Multivariate species differences in morphology,kinematics, and forcePrior to multivariate analyses, all variables werestandardized to a mean of zero and a variance of one.This placed all variables on the same scale and elimi-nated the problem of variables on larger scales havinga larger influence on the results than variables onsmaller scales (Quinn & Keough, 2002).

Each of the levels of analysis contained numerousinter-correlated variables, which can be a majorproblem for multivariate analyses. We addressed thisissue in two ways. For, morphological and kinematicvariables we conducted separate principal compo-nents analyses (PCA) to reduce the dimensionality ofthe data to a few PCs that describe the most of thevariation in morphological or kinematic variables. Bydefinition, the PC axes are orthogonal and uncorre-lated, thus removing the effect of collinearity in thedata prior to further multivariate analysis (seebelow). PCs were considered significant if they hadeigenvalues > 1 and had a percentage variationexplained greater than that expected by the brokenstick model (Quinn & Keough, 2002). Only significantPC axes were used in subsequent multivariateanalyses.

The PCA on the force variables was not useful foraddressing collinearity because it generated numer-ous ‘significant’ axes that explained small fractionsof the variance in the force data. Therefore, weaddressed collinearity in the force data by eliminatinghighly inter-correlated variables from multivariateanalysis (Quinn & Keough, 2002). Whole bodyimpulses were always highly correlated with wholebody peak forces in each direction (r > 0.65) andbraking impulses/forces were highly correlated withaccelerative impulses/forces (because animals weremoving at near-steady speed). Thus, the reduced dataset included only seven variables: vertical, accelera-tive, and lateral impulses, and the relative timeto peak vertical, braking, lateral, and braking–accelerative transition. Force variables in thisreduced data set had weak correlations (r < 0.40),indicating that collinearity would not be problematicin subsequent multivariate analyses. Thus, the mul-tivariate analyses of species differences used PC axesfor morphology, kinematics and a reduced force dataset (seven variables).

Discriminant function analysis (DFA) was usedat each level (morphology, kinematics and force) todetermine statistical differences among species inmultivariate space. DFA extracts axes that are linearcombinations of the original variables that maximizethe probability of correctly assigning the data to pre-determined groups (Quinn & Keough, 2002). SeparateDFAs were run on morphology, kinematics, and forcelevels with species as the predetermined groups.



Standardized discriminant coefficients were used todetermine the relationship between discriminant axesand the PC axes (morphology and kinematics) ororiginal variables (forces). Differences among specieson each level were identified by computing Mahalano-bis distances (D2) and associated F-statistics and sig-nificance tests between species centroids for DF1 and2 (SAS Institute, 2001). Species that were not signifi-cantly different were placed in the same group;whereas species that were significantly different wereplaced in different groups.

Relationships between multivariate levels(morphology, kinematics, and force)After summarizing the differences between species ateach level, three approaches were used to examinerelationships among species between morphological,kinematic, and force levels. First, a qualitativecomparison of relationships among levels was per-formed visually by comparing relative positions ofsignificantly different groups at each multivariatelevel (Reilly & Lauder, 1992). Second, a Manteltest assessed significant multivariate correlationsbetween each level. The Mantel test compared matri-ces of Mahalanobis distances between the centroids ofeach species in discriminant space at one level withthose of another level. The software ZT (Bonnet &Van de Peer, 2002) was used to generate 5000 ran-domizations to compute the correlation between: (1)morphology and kinematics, (2) kinematics and force,and (3) morphology and force. A significant Manteltests indicates correlation between levels, but doesnot specify which aspects of morphology, kinematics,or force drive the correlation. Third, to identify whichvariables are correlated across levels, separatemultiple regressions were computed between the first(and second) discriminant axes across levels. In thistest, the morphology and kinematic levels were inde-pendent variables, whereas force was the dependentvariable. Species values for multiple regressions weretheir mean scores on each discriminant axis. Thecombination of these three techniques allowed for thethorough examination of the relationship betweenspecies position in multivariate space at differentlevels of the analysis.

Finally, we employed partial least squares to testfor relationships between: (1) morphology and kine-matics and (2) kinematics and force. Partial leastsquares is ideal for this data set because (1) thesedata violated some of the assumptions of discriminantanalysis (equal group sizes and variances) and (2)collinearity can be explicitly handled without usingPCs or eliminating variables allowing for the directestimation of the relationship of each variablebetween levels. Species mean values for each variablewere used as input for the analysis. We used cross-

validation to avoid over-fitting the data and to deter-mine the number of factors to keep in the finalanalysis.

Effect of phylogenyThe evolutionary relationships among species makethem non-independent data points; thus, traditionalstatistical analyses are clouded by phylogeny (Felsen-stein, 1985). To control for the effects of phylogeny, wecomputed independent contrasts (Garland, Harvey& Ives, 1992) in the PDAP module of MESQUITE(Midford, Garland & Maddison, 2002; Maddison &Maddison, 2007) between species means on the firstdiscriminant axis for each level. There was no rela-tionship between the absolute values of standardizedcontrasts and their standard deviation, indicatingthat the contrasts were adequately standardized(Garland et al., 1992). Thus, we re-ran the multipleregression with the independent contrasts of each ofthe first discriminant axes. The regression was forcedthrough the origin (Garland et al., 1992). A significantmultiple regression would indicate that species scoreson the first discriminant axis have undergone corre-lated evolution. The Townsend et al. (2004) phylogenywas use for all analyses (Fig. 3). Branch lengths wereunavailable; therefore, we set all branch lengths toone, which does not substantially impact the outcomeof phylogenetic comparative analyses (Diaz-Uriarte &Garland, 1998), nor the outcome of similar studies oflizard locomotor function (McElroy, Hickey & Reilly,2008).

Finally, squared-change parsimony in MESQUITE(Maddison & Maddison, 2007) and maximum likeli-hood (ML) in ANCML (Schluter et al., 1997) were bothimplemented to calculate the ancestral characterstates of species mean scores on DF1 and DF2 formorphology, kinematics, and force. We used bothtechniques because squared-changed parsimony cancalculate ancestral states for phylogenies withpolytomies (sensu the phylogeny of Townsend et al.,2004; Fig. 1), whereas, ML cannot handle polytomiesbut can calculate standard errors and confidenceintervals (CIs) around nodal estimates. For ML, weaddressed polytomies by examining all possible reso-lutions; however, different resolutions did not mate-rially alter the results. Squared change parsimonyancestral states were then plotted in discriminantspace at each functional level. ML 95% CIs were usedto infer significant evolutionary shifts (McElroy et al.,2008).

RESULTSMULTIVARIATE PATTERNS IN LOCOMOTOR LEVELS

MorphologyThe PCA on size-corrected morphological variablesextracted two axes that together explained 80% of



the morphological variance (Table 2). PC1 explained70% of the variance in morphology and had uniformmoderate positive loadings for all morphologicalvariables (except pelvic length), indicating that alllimb segmental lengths and pelvic width increasedin relative size along PC1. Thus, species with posi-tive values on PC1 had relatively longer fore andhindlimbs, whereas species that had negativevalues had relatively shorter fore and hind limbsrelative to their size. PC2 explained 10% of themorphological variance and had a strong positiveloading for pelvis length. Thus, species with positivevalues on PC2 had relatively long pelves, whereasspecies with negative values had relatively shortpelves.

The DFA on these two morphological principal com-ponents extracted two axes (Fig. 4) explaining 93% ofthe variation in morphology (Table 2) and indicatedthat there are statistically significant differencesbetween species (Wilk’s l = 0.020, F18,388 = 65.1,P < 0.0001). DF1 and 2 closely approximated principalcomponents 1 and 2, respectively, because each PCaxis variable scored large and positively on only onediscriminant axis (Table 2). Thus, PC loadings formorphological variables could be interpreted alongthe DF axes with DF1 being related to relative limblength (relatively longer limbs had large positivevalues) and DF2 being related to relative pelvic

length (relatively longer pelves had large positivevalues). Mahalanobis distances between species cen-troids revealed that all of the species were signifi-cantly different in morphospace (all P < 0.0001).Species lined up on DF1 from the relatively shortestlimbs of the skink (Eulamprus) through the relativelyaverage limbs in the Varanid (Varanus), Lacertid(Acanthodactylus), and the Gerrhosaurid (Trachelop-tychus), to the relatively longest limbs in theIguanians (Tropidurus, Oplurus, and Laudakia).Tracheloptychus (a Gerrhosaurid) had a relative limblength similar to Acanthodactylus and Varanus butwas significantly different on DF2, revealing its novelextremely long pelvis.

KinematicsThe first two PCs of the size- and speed-correctedkinematic variables together explained 96% of thevariance in kinematics (Table 3) and were clearlycorrelated with different variables. PC1 explained58% of the kinematic variance and had a large posi-tive loading for stride length and a large negativeloading for stride frequency. Thus, species with posi-tive values on PC1 took relatively long strides at lowstride frequencies, whereas species with negativevalues took relatively short strides at high stridefrequencies. PC2 explained 38% of the kinematic vari-ance and had a strong positive loading for float dis-

Table 2. Results of the multivariate morphological analysis

Morphological PCA Morphological DFA

PC1 PC2 DF1 DF2

Eigenvalue 10.47 1.49 Eigenvalue 9.42 1.61% Variance 70% 10% % Variance 79% 14%Humerus 0.29 -0.02 PC1 9.03 0.01Ulna 0.28 -0.11 PC2 1.97 9.50Carpals 0.19 -0.34Third metacarpal 0.28 -0.20Third toe 0.25 -0.15Pectoral width 0.27 0.06Femur 0.30 0.06Tibia 0.30 -0.01Tarsals 0.24 -0.14Fourth metatarsal 0.29 0.06Fourth toe 0.21 0.41Fifth metatarsal 0.27 -0.13Fifth toe 0.28 0.15Pelvic width 0.27 0.21Pelvic length 0.04 0.73

Loadings are calculated between each principal component and each kinematic variable. Standardized coefficients arecalculated between each discriminant axis and each principal component.PCA, principle componemt analysis; DFA, discriminant function analysis.



tance and a strong negative loading for step length.Thus, species with positive values on PC2 had stridescharacterized by relatively short steps and long floatdistances, whereas species with negative values hadstrides characterized by relatively long steps andshort float distances.

The DFA on these two kinematic principal compo-nent axes extracted two axes that explained 99% of

the kinematic variation (Table 3). DF1 and 2 werehighly correlated with PC1 and 2, respectively, basedon large and positive loadings (Table 3). Therefore,the DF axes could be related to the original kinematicvariables: large scores on DF1 depict species withrelatively long stride length and low stride frequency,whereas small scores represent relatively shortstrides at high frequency. Large scores on DF2

Figure 4. Bivariate plot of the first two discriminant axes for morphology, kinematics, and forces. The percentagevariation explained is labelled with each axis. The variables with the largest coefficients on each axis (from Tables 3, 4,5) are labelled opposite to that axis. Values for squared change parsimony ancestral reconstructions for nodes (A–E fromFig. 1) are plotted on each level.



describe species taking relatively short steps withlong floats, whereas small scores depict species tak-ing relatively long steps with short floats. Specieswere significantly different in DF (Wilks’ l = 0.423,F12,124 = 5.54, P < 0.0001) with Mahalanobis distancesshowing that the species clustered into two differentgroups [P within groups, range 0.071–0.725 (exceptTropidurus, see below), P between groups, range0.001–0.047] in kinematic space (Fig. 4). Eulamprus,Varanus, and Tracheloptychus clustered together andwere characterized by relatively short strides at highfrequency and intermediate step length and floatdistance. Oplurus, Acanthodactylus, Laudakia, andTropidurus clustered in the other group with rela-tively long strides at lower frequency with longersteps and shorter float distances, except Tropidurusthat exhibited relatively short steps with large floatdistances (Mahalanobis significance, Tropidurus toLaudakia, P = 0.071; to Oplurus, P < 0.001; to Acan-thodactylus, P = 0.0120).

ForcesThe DFA on the reduced set of size- and speed-corrected whole body force variables extracted twoaxes that explained 74% of the force variance (Table 4).DF1 accounted for 49% of the force variance and had alarge positive score for relative vertical impulse andrelatively weak scores for all other variables (Table 4).Because of the significant correlation between relativevertical impulse and relative peak vertical force(r = 0.709, P < 0.00001), we interpreted this axis asrepresentative of both of these vertical force variables.Time to peak vertical force was not correlated withvertical impulse (r = -0.182, P = 0.132) or peak verticalforce (r = -0.054, P = 0.658). DF2 accounted for 25% ofthe force variance and had a large positive score for therelative timing of the braking–accelerative transitionand accelerative impulse (Table 4). Species weresignificantly different (Wilk’s l = 0.246, F42,271 = 2.25,

P < 0.0001) with Mahalanobis distances demonstrat-ing that species clustered into two different groups inforce space (Fig. 5). Eulamprus with the smallestrelative vertical forces and impulses was significantlydifferent from the rest of the species (Mahalanobis’significance P range = 0.001–0.038), which exhibitedrelatively larger vertical forces and impulses. Theextremes of this group on DF1 (Tropidurus and Tra-cheloptychus) also had large scores on DF2. Thesetwo species positions approached significance (Mahal-anobis’ significance: Tropidurus to AcanthodactylusP = 0.133, to other species P < 0.050; Tracheloptychusto Acanthodactylus P = 0.095, to other speciesP < 0.050), indicating larger times to the braking–acceleration transition and larger accelerative impulsecompared to the rest of the group.

RELATIONSHIPS BETWEEN MULTIVARIATE LEVELS

The a priori model of the causal links for terrestriallocomotion predicted that morphological variation

Table 3. Results of the multivariate kinematic analysis

Kinematics PCA Kinematics DFA

PC1 PC2 DF1 DF2

Eigenvalue 2.32 1.53 Eigenvalue 0.83 0.29% Variance 58% 38% % Variance 74% 26%Stride length 0.64 0.03 PC1 0.85 0.06Stride frequency -0.64 -0.04 PC2 -0.04 0.88Step length 0.26 -0.73Float distance 0.34 0.68

Loadings are calculated between each principal component and each kinematic variable. Standardized coefficients arecalculated between each discriminant function axis and each principal component axis.PCA, principle componemt analysis; DFA, discriminant function analysis.

Table 4. Results of the discriminant function analysis ofwhole body force data

DF1 DF2

Eigenvalue 0.85 0.45% Variance 49% 25%Vertical impulse 1.29 0.05Accelerative impulse 0.05 0.57Lateral impulse 0.07 0.04Time peak vertical force 0.22 -0.01Time braking–accelerative transition -0.45 1.12Time peak braking force -0.01 0.02Time peak lateral force -0.31 -0.05

Standardized coefficients are calculated between each dis-criminant function (DF) axis and each whole body forcevariable.



should predict kinematic variation, which, in turn,should predict force variation (Reilly et al., 2007). Toexamine the relationships between levels, we createda three-dimensional plot that stacked each of the

multivariate levels (Reilly & Lauder, 1992) alignedalong the major axes of variation (DF1 and 2). Then,we examined relative positions of species betweenmorphological and kinematic levels and then between

Figure 5. Visualization of the multivariate relationship between morphology, kinematics, and whole body force in theseven lizard species from the present study plotted sensu Reilly & Lauder (1992). Each plane represents the discriminantspace for each level of analysis (from Figs 4, 5, 6) with ellipses surrounding groups at each level determined byMahalanobis distances and associated F-tests. Lines connect species’ centroids between levels. Note that the lines arealmost vertical, indicating correspondence in species position on the first discriminant axis on each level. DF, discriminantfunction.



kinematic and force levels (Fig. 5). Specifically,species were related between levels:

1. Eulamprus was positioned on the left at each leveland was significantly different from all otherspecies on the morphology and force, but not kine-matics levels. It was characterized by relativelyshort limbs, short stride length, high stride fre-quency, and small vertical impulse and peak force.

2. Tropidurus was positioned on the right at eachlevel and approached statistically significant dif-ferences from other species at the kinematic andforce levels. It had relatively long limbs, longstride length, low stride frequency, and large ver-tical impulse and peak force. Tropidurus also hadthat longest float distance and shortest step lengthof any species in the present study.

3. Varanus and Tracheloptychus were positioned cen-trally on all three levels, with both having legs ofmoderate length and intermediate stride lengthand frequency. However, Varanus had a shortpelvis and fourth toe whereas Tracheloptychushad a long pelvis and fourth toe and this differ-ence seemed to manifest itself in Varanus havingrelatively smaller accelerative impulse andan earlier braking–accelerative transition thanTracheloptychus.

4. Oplurus and Laudakia were positioned on theright in morphological space but centrally in kine-matic and force spaces. These species had rela-tively long legs, long stride length and low stridefrequency, and moderate-to-large vertical impulseand peak force. Although it had relatively shorterlimbs, Acanthodactylus clustered together withthese species at both the kinematic and forcelevels.

More generally, comparisons across levels suggest alinear spread corresponding to the first discriminantaxis on each level. Species position on DF1 at themorphological level generally corresponds to theirposition on DF1 at the kinematic level and at the

force level. Thus, increasing relative limb length cor-responds to increasing relative stride lengths andlower stride frequencies. Similarly, increasing relativestride lengths and lower stride frequencies arerelated to increasing relative vertical forces andimpulses. Three statistical tests of these relationshipsconfirm these integrative patterns.

First, the Mantel tests indicated a significant posi-tive correlation between the morphological and thekinematic levels (R = 0.78, P = 0.0120; Table 5) andbetween the kinematic and force levels (R = 0.88,P = 0.0004, Table 5). Together, these results show thatthere is a significant multivariate correlation betweenspecies position in morphological, kinematic, andforce discriminant spaces.

Second, to uncover which variables were drivingthe multivariate correlations between levels, we ran amultiple regression testing for the effects of morphol-ogy and kinematics as a predictor of force. The mul-tiple regression revealed that the morphological andkinematic levels combined to become an excellentpredictor of species’ centroid position on the forcelevel for DF1 (R2 = 0.87, F2,4 = 13.26, P = 0.017) butnot on the DF2 (R2 = 0.44, F2,4 = 1.58, P = 0.38). Thus,there is a statistically significant relationshipbetween limb length, stride length and frequency, andvertical forces and impulses (Fig. 6).

The results of the partial least squares analysiswere similar to the results of the multiple regressionsbased on DF axes. There was one factor betweenmorphology and kinematics. This factor accounted for81% of the morphological variation and explained14% of the kinematic variation. The model coefficientsindicated a positive relationship between limb skel-etal element lengths (except pelvis length) and stridelength but a negative relationship with stride fre-quency. Thus, species with longer limbs ran withlonger strides at low frequency, whereas species withshorter limbs ran with shorter strides at high fre-quency. There was one factor between kinematics andforce. This factor accounted for 49% of the kinematic

Table 5. Results of Mantel tests for the multivariate correlation between species position in discriminant function spaceat each level of analysis

Kinematics(velocity)

Kinematics(dimensionless)

Force(velocity)

Force(dimensionless)

Morphology 0.66** 0.66** 0.84*** 0.60**Force (velocity) 0.79*** – – –Force (dimensionless) – 0.59** – –

*P < 0.05, **P < 0.01, ***P < 0.001.Statistical significance was determined by a randomization procedure. Correlations were calculated for velocity correctedand dimensionless speed corrected data (indicated in parentheses).



variation and explained 32% of the force variation.The model coefficients described a positive relation-ship between stride length and float distance and allimpulses and peak forces, and a negative relationshipbetween stride frequency and all impulses and peakforces. The signs of the coefficients between forcevariables and stride length were equal in magnitudeand opposite in sign to those for stride frequency.Thus, species taking longer strides with longer float

distances at low stride frequency exhibited greatermagnitude ground reaction forces, whereas specieswith shorter strides and float distances at higherstride frequency exhibiter smaller ground reactionforce.

Finally, to account for the effect of phylogeny on therelationship between multivariate levels, we re-ranthe multiple regression on the independent contrastsfor species centroids position on DF1. The indepen-

Figure 6. Three-dimensional plot of the first discriminant axis at each level of analysis. Data points are species’ meanson the first discriminant axis for each level. The bold line (best fit line from multiple regression) highlights the tightrelationship between species position along on the first discriminant axis. Long-limbed species take longer strides at lowerfrequency, resulting in large vertical whole body forces and impulses. We plotted an inverted version of the phylogeny ofTownsend et al. (2004), in which tips corresponded to species position in multivariate space, and then mapped multi-variate patterns of character evolution onto the phylogeny; for further details, see Discussion. Black and grey bars areevolutionary trends on DF1 and 2, respectively, which have resulted in convergence. *Statistically significant evolutionarytransition.



dent contrasts multiple regression revealed thatmorphology, kinematics, and force have undergonecorrelated evolution (R2 = 0.86, F2,3 = 9.35, P = 0.050).This indicates that species evolving relatively longerlimbs also evolve relatively longer strides at lowerfrequency and relatively large vertical forces andimpulses. This relationship is plotted in Figure 6 withthe phylogeny of the study species superimposed onthe three-dimensional relationships of morphology,kinematics and force on DF1. Squared change parsi-mony ancestral node reconstructions are plotted inmultivariate space in Figure 4. CIs from ML ancestralcharacter estimates indicated that only the transitionto a longer pelvis and fourth toe in Tracheloptychusfrom its ancestor was statistically significant. Thissignificant transition and other nonsignificant trendssuggested by ancestor character reconstruction areplotted in Figure 6.

DISCUSSION

The present study aimed to examine the multivariaterelationships between morphology, kinematics, andforce variation during running in lizards. Theseanalyses show that these three levels of locomotorfunction have tight functional and evolutionary rela-tionships (Figs 4, 5, 6, Table 6). In lizards, morpho-logical variation predicts kinematic variation, which,in turn, predicts force variation.

LIMB MORPHOLOGY AND STRIDE KINEMATICS

A key issue in animal locomotion is how limb lengtheffects stride kinematics after accounting for differ-ences in size and speed (Strang & Steudel, 1990). One

of our principal findings was that lizard limb lengthhas a significant linear relationship with stridekinematics: as limb length increases, stride lengthincreases and stride frequency decreases (Figs 5, 6).This finding was not surprising given that it is gen-erally known across a range of animals (Strang &Steudel, 1990) and has been shown within severallizard families (Teiidae: White & Anderson, 1994;Phrynostomatidae and a single teiid: Irschick &Jayne, 1999; Lacertidae: Vanhooydonck et al., 2002).However, the present study shows that a strongrelationship between limb morphology and strideparameters holds across a greater portion of themorphological diversity of lizards even after control-ling for phylogeny.

These data also allowed us to examine potentialtrade-offs between how differing morphologies modu-late stride length and stride frequency to movequickly. To examine potential trade-offs in the rela-tionship between limb length and speed modulation,we calculated the slopes from least-squares linearregressions for the relationships between runningspeed and raw stride length or stride frequency(Table 6). This analysis shows that the relativelyshortest-limbed species (Eulamprus) modulates onlystride frequency, whereas the one of the longest-limbed species (Tropidurus) modulates only stridelength to increase speed, and the intermediate limbedspecies (except Tracheloptychus) modulate both. Tra-cheloptychus has average size limbs but relies on astride length only modulation strategy. This may bebecause Tracheloptychus has an inordinately longerpelvis and fourth toe length (Fig. 4) and the fourth toehas been shown to be an important correlate of stridelength (Irschick & Jayne, 1999). Oplurus has rela-tively long limbs but modulates both stride frequencyand stride length. Although it is unclear why thisspecies does not use primarily stride length modula-tion, it is clear that, for its size, Oplurus exhibitsrelatively slow maximum sprint speed and the short-est float distance, and this may be related to itsdeviation from the proposed pattern in lizards.Overall, these data support previous studies indicat-ing the tight correlation between limb length andstride length/frequency modulation in lizards (White& Anderson, 1994; Vanhooydonck et al., 2002). Inaddition, our data support the hypothesis thatanimals modulate stride frequency, stride length, orboth, to increase speed (Biewener, 2003). However,this is the first time that the extremes in limb lengthare found to be related to the reliance on modulationof only one parameter to increase speed. Our data donot address exactly how limb kinematics (e.g. limbprotraction and retraction) are related to species dif-ferences in speed modulation strategy; future studiesshould address this issue.

Table 6. Regression parameters showing the relationshipbetween raw stride kinematics and speeds for the sevenlizard species

Species

Stride length Stride frequency

Slope Intercept Slope Intercept

Acanthodactylus 0.65* -0.60 0.89* 0.66Eulamprus 0.02 -0.82 1.99* 1.10Laudakia 0.80* 0.37 0.52* -0.51Oplurus 0.40* 0.24 0.86* -0.32Tracheloptychus 1.38* -0.94 -0.17 1.13Tropidurus 1.27* -0.27 0.23 -0.01Varanus 0.37* 1.02 0.89* -1.02

*Statistical significance (P < 0.05) of regression slopes wasdetermined by t-tests.



STRIDE KINEMATICS AND WHOLE BODY

VERTICAL FORCE

It is important to emphasize that we are discussingvertical impulses integrated over the support phasefor a limb pair, as opposed to over the entire stride(Fig. 3). Although it is well known that vertical forcessummed (vertical impulse) over the entire stridedivided by stride time must equal body weight (Bie-wener, 2003) and they do over a stride in all speciesin this study (Fig. 7), this was not a focus of thepresent study. Rather, we were interested in howspecies modulate forces over the support phase ofdiagonal couplets during running to effectivelysupport and propel the body in a sample of morpho-logically and kinematically diverse lizard species.

The multivariate analyses of locomotor functionrevealed a significant correspondence between limblength, stride kinematics, and whole body forces(Figs 5, 6; Table 5). Species with longer limbs tookrelatively longer stride lengths, shorter stride dura-

tions, and applied relatively larger peak whole bodyvertical forces and vertical impulses to the ground.For example, among lizards moving at speeds acrosstheir locomotor scope, the long-limbed Tropidurus hadstride frequencies that were approximately one-halfless, and vertical impulses (summed over supportduration) that were approximately two-fold greater,than those of short-limbed but equivalently-sizedEulamprus. Figure 7 presents the representative ver-tical forces from these two species that clearly illus-trate how morphology, kinematics, and force arerelated. The other species of lizards fell between thesetwo extremes. As expected, the relationship betweenstride kinematics and vertical forces exhibited bythese lizards is in accordance with well-known bio-mechanical principles (Biewener, 2003). However,these data on running lizards clearly demonstratethat the relationship between kinematics and verticalforce is driven by the underlying limb morphologicalvariation and that lizards with shorter limbs must

Figure 7. Sample vertical forces that illustrate how the longest and shortest-limbed lizards in the present study variedin kinematics and whole body forces. These two trials were from individuals of similar mass and speed; thus, the raw dataare presented. L and R, left or right leg supports, respectively. A, Tropidurus torquatus: speed = 1.99 m s-1; mass, 27 g;snout–vent length = 91 cm; hindlimb length, 70 cm; forelimb length = 49 cm; stride frequency = 6.2 s-1; stridelength = 28 cm; peak vertical force = 0.82 N; vertical impulse = 0.0163 Ns. (B) Eulamprus quoyii: speed = 1.92 m s-1;mass = 21 g; snout–vent length = 98 cm; hindlimb length = 46 cm; forelimb length = 31 cm; stride frequency = 14 s-1; stridelength = 14 cm; peak vertical force = 0.36 N; vertical impulse = 0.0061 Ns. The approximate doubling of stride frequencyin the short-limbed Eulamprus results in an approximate halving of the peak vertical force and vertical impulse comparedto the long-limbed Tropidurus. LH, RF: left hindlimb – right forelimb couplet step; RH, LF: right hindlimb – forelimbcouplet step.



use kinematic compensation to effectively supportbody weight. Overall, short-limbed species cycle theirshort legs more often with less force per supportwhereas long-limbed species cycle their long legs lessoften with more force per support all so that eachspecies have their forces sum to body weight overtheir entire strides (Fig. 7). This finding supports theprediction of previous studies based on kinematics(Van Damme et al., 1998; Aerts et al., 2000).

Energetic implicationsThese findings may have important implications forthe energetics of lizard locomotion. Van Damme et al.(1998) suggested that short stride –high frequencyspecies should expend a large amount of metabolicenergy because they must perform a lot of internalmechanical work to cycle the limbs. However, VanDamme et al. (1998) also point out that long stride–low frequency species will produce a large amount offorce, which will also increase metabolic expenditure.Although we did not directly measure metabolicexpenditure, our species appear to fall along a con-tinuum, with the Iguanians (Tropidurus, Oplurus,and Laudakia) producing very large forces butmoving at very low stride frequency, Acanthodactylus,Varanus, and Tracheloptychus producing intermedi-ate amounts of force and stride kinematics, and theskink (Eulamprus) moving at very high stridefrequency but with small forces (Figs 5, 7). Thiscontinuum suggests that species with very long(Iguanians) or very short (skinks) limbs may engagein the most costly locomotion; whereas species withintermediate-sized limbs (Acanthodactylus, Varanus,and Tracheloptychus) may engage in less costly loco-motion. The cost of locomotion for running in erectbirds and mammals is largely determined by thesethree levels of locomotor function (Roberts et al.,1998; Pontzer, 2005, 2007). Examination of how thecost of locomotion is related to these levels of locomo-tor function in sprawling animals (i.e. turtle, lizards,alligators, and salamanders) would be a useful.

It is intriguing that, given the above argument, thehigh-cost species are sit-and-wait foragers (Tropidu-rus, Oplurus, Laudakia, and Eulamprus) whereas thelow-cost species are wide foragers (Acanthodactylus,Varanus, and Tracheloptychus). This suggests that,similar to so many other phenotypic traits (Reilly et al.,2007), foraging behaviour may be driving locomotorfunctional morphology and energetics in lizards (seealso, Clemente, Withers & Thompson, 2009).

Propulsive forcesInterestingly, Tracheloptychus and Tropidurus hadthe largest values on both kinematic and force DF2,

indicating that they had the largest relative floatdistances, the latest braking–acceleration transitiontimes, and the largest accelerative impulses. Thus,these two species are delivering larger, more focusedaccelerative forces late during the support phase inorder to generate longer float distances. Morphologi-cally, this may be related to the novel longer pelvis inTracheloptychus but there is no clear morphologicalexplanation for the same pattern in Tropidurus. Inaddition, the ability to deliver more focused accelera-tive forces to produce longer float distances appears tobe a correlate of a stride length speed modulationstrategy because Tropidurus and Tracheloptychuswere the only two species to rely solely on stridelength to increase speed. Aside from these multivari-ate patterns, longer float distances were correlatedwith both larger vertical whole body force (Pearsonproduct-moment correlations data pooled acrossall species: float distance – vertical impulse: r = 0.38,P = 0.001; maximum vertical whole body force:r = 0.23, P = 0.05) and larger accelerative whole bodyforces (accelerative impulse: r = 0.33, P = 0.006;maximum accelerative whole body force: r = 0.34,P = 0.004). Species that incorporate float phases areessentially producing alternating single-leg jumps inwhich the centre of mass (COM) is propelled ballisti-cally with each step. This suggests that species thatfloat over greater distances produce more vertical andaccelerative forces to effectively propel the COM upand forward during this ‘jump’.

EVOLUTIONARY TRENDS IN LIZARD LOCOMOTOR

FUNCTIONAL MORPHOLOGY

The mapped characters on the inverted phylogeny inFigure 6 summarize the evolutionary trends in limblength, stride kinematics, and ground reaction forcesin lizards. The putative ancestor (node A) had rela-tively short limbs, short high-frequency strides, andintermediate vertical forces (Figs 4, 6). From theseancestral traits, lizards diverged along two separateevolutionary trajectories, principally based on diver-gence along DF1. Tracheloptychus and Eulamprusexhibit an evolutionary trend towards even shorterlimbs, shorter strides at higher frequency, and lowervertical forces (Node B and tip values); whereas thenodes (C, D, E) leading to Varanus, Acanthodactylus,and the Iguanians showed an evolutionary trendtowards longer limbs, longer low-frequency strides,and larger vertical force. From its ancestor (node D),the Iguania evolved to the functional extreme with thelongest limbs, longest strides at the lowest frequency,and largest vertical forces, whereas Eulamprushas evolved to the extreme in the opposite direction.Taken together, these data show that deep phyloge-



netic effects (locomotor functional split at node A)are imprinted upon locomotor functional evolution,which is a finding in agreement with evolutionarytransitions in many other lizard traits (e.g. headmorphology: McBrayer & Corbin, 2007; diet: Vitt &Pianka, 2007; feeding kinematics: Reilly & McBrayer,2007; chemosensory systems: Cooper, 2004).

Several cases of evolutionary convergence areevident within the two overarching trends in lizardlocomotor evolution. Varanus has converged with Tra-cheloptychus and Eulamprus with its short limbs andshort high-frequency strides. However, Varanus hasnot converged in vertical force dynamics, which maybe related to morphological changes that enhancebipedal posturing in this genus (Schuett, Reiserer &Earley, 2009). Oplurus has reverted to having some-what shorter, faster strides and this may be related tothis species being relatively slow for its size. Finally,Tracheloptychus and Tropidurus exhibit convergencealong DF2, evolving longer float distances, shortersteps, later braking–accelerative transition times,and larger accelerative impulses than their ancestorsand, although this may be related to longer pelvic andfourth toe morphology in Tracheloptychus, the reasonfor this in Tropidurus remains unclear. Thus, locomo-tor functional evolution clearly exhibits some flexibil-ity. Future studies should explore how evolutionaryflexibility in finer details of locomotor function isrelated to specific aspects of ecology, habitat use, andbehaviour.

ACKNOWLEDGEMENTS

We thank Emily Bevis, Caityln Cato, Alex Fotis, BaileyMiles, Andy Parchman, and Kristen Stover for theirassistance with data collection and analysis. JohnBertram, David Lee, Audrone Biknevicius, AndrewLammers, and Kay Earls provided advice and encour-agement regarding the function of our force platforms.Robbie Wilson kindly helped us acquire permits fromthe Queensland government of Australia to work onEulamprus. Jens Vindum and Bob Drewes (CaliforniaAcademy of Sciences), Robert Espinosa (CaliforniaState University at Northridge), Steve Rodgers (Car-negie Museum), and Jim McGuire (University of Cali-fornia Museum of Vertebrate Zoology) kindly loanedlizard specimens for morphological study. Joe Eastmangraciously allowed us to use his X-ray machine anddeveloping equipment. Audrone Biknevicius, AngelaHorner, Mike Jorgenson, Don Miles, and Gar Rothwellprovided comments that greatly improved the qualityof the manuscript. This research was funded by NSFgrants (IBN 9727212; IBN 0080158; IOB 0520100) andOhio University Research Challenge grant to S.M.R.,and an Ohio Center for Ecology and EvolutionaryBiology Fellowship to E.J.M.

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APPENDIXMUSEUM CODES

Museum abbreviations: CAS, California Academyof Sciences; CSUN, California State University atNorthridge; CM, Carnegie Museum; UCMVZ, Univer-sity of California Museum of Vertebrate Zoology.

Acanthodactylus boskianus: CAS (9723, 9709, 9710,9708, 138659, 138657, 138658, 138655, 138120,138724, 138722, 138723, 138721, 13871, 138718), CM(56708, 56648, 56569, 56662, 56756, 56597, 56566,56643, 56761, 56760, 56612, 56649, 56567, 56661,56568).

Eulamprus quoyii: CAS (76873, 76879, 76830, 76822,76850, 76868, 76827, 76853, 76845, 76826, 76860,76880, 76843, 76824, 76868, 76867, 76847, 76877,76825, 76872, 76858, 76862, 76842, 76852, 76835,76851, 76848, 76818, 76854).

Laudakia stellio: CAS (217951, 217952, 217874,217875, 217683, 217876, 217685, 217684, 218089,218090, 217985, 218091, 5007, 2992, 217987, 217984,217711, 217709, 217807, 217808, 217809, 217710,217712, 217803, 217802, 217804, 218005, 218092,217680, 217980); three uncataloged individuals fromOhio University.Oplurus cuvieri: CAS (12777, 126358, 135152, 13951,13957, 13953, 13950); UCMVZ (238792, 128904,238791, 238793, 117597, 21117, 238794, 247486,238795, 238790, 238796); three uncataloged individu-als from Ohio University.Tracheloptychus petersi: CSUN (1213); UCMVZ(238766, 238764, 238765, 238768, 238767); sixuncataloged individuals from Ohio University.Tropidurus torquatus: CM (136154, 136117, 64888,943, 4594, 7411); one uncataloged individual fromOhio University.Varanus exanthematicus: CM (24705, 24700, 15163);CSUN (1417, 2903); UCMVZ (75661); CAS (169935,139504, 103109, 130091); three uncataloged individu-als from Ohio University.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Table S1. Pearson product-moment correlation coefficients between morphological, kinematic, and whole bodyforce variables and body size (snout–vent length or mass) and speed.

Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materialssupplied by the authors. Any queries (other than missing material) should be directed to the correspondingauthor for the article.



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